The invention described herein was made by employees of the United States Government and may be manufactured and used by or for the Government for governmental purposes without the payment of any royalties thereon or therefor.
1. Technical Field
The present invention is directed toward an improved method and system for design optimization using composite response surfaces. These composite response surfaces are constructed by combining neural networks with other interpolation/estimation techniques such as polynomial fits. In particular, the present invention relates to a flexible process for the efficient use of simulation and experimental data in aerodynamic design optimization.
2. Description of the Related Art
Considerable advances have been made in the past two decades in developing advanced techniques for the numerical simulation of fluid flows over aerodynamic configurations. These techniques have now reached a level of maturity where they can be used routinely, in conjunction with experiments, in aerodynamic design. However, aerodynamic design optimization procedures that make efficient use of these advanced techniques are still in their infancy.
The design of aerodynamic components of aircraft, such as wings or engines, involves a process of obtaining the most optimal component shape that can deliver the desired level of -component performance, subject to various constraints, e.g., total weight or cost, that the component must satisfy. Aerodynamic design can thus be formulated as an optimization problem that involves the minimization of an objective function subject to constraints. A variety of formal optimization methods have been developed in the past and applied to aerodynamic design. These include inverse design methods, adjoint methods, sensitivity derivative-based methods, and traditional response surface methodology (RSM).
Inverse design methods, as the name suggests, are strictly used for inverse design (for example, to design a wing that produces a prescribed pressure distribution). The known inverse design methods do not take into account the viscosity of the fluid and are therefore used in preliminary design only. This method is applicable to a small class of aerodynamic design problems, such as those where the entire pressure distribution can be specified a priori.
Adjoint methods provide the designer with the gradient of the objective function that is being minimized in order to obtain the optimal design. Starting from an initial component shape that is reasonable, the design space is searched using this gradient information. The main advantage of this method is that the gradient information is obtained very rapidly. However, the method has several shortcomings. It is difficult to use this method to arrive at an optimal design when several engineering disciplines (such as, aerodynamics, structures, and heat transfer) need to be considered simultaneously. It requires a completely different formulation for every discipline and for every set of governing equations within each discipline. It is also difficult to rapidly evaluate design tradeoffs which require that the constraints be changed many times. It is also not possible to use existing design or experimental data, or partial or unstructured sets of data, to influence the design process.
Sensitivity derivative-based methods typically require that many aerodynamic solutions be obtained in order to compute the gradient of the objective function. As the number of design parameters increases, these methods can become computationally expensive to use. They are also sensitive to any noise in the design data sets. Additionally, like the adjoint methods, it is not always possible to use existing design or experimental data, or partial or unstructured sets of data, to influence the design process. Design tradeoff studies require that additional aerodynamic simulations be performed, thus incurring additional expense. However, they are applicable to a wide range of aerodynamic design problems.
Response surface methodology (RSM) represents a framework for obtaining optimal designs using statistical methods such as regression analysis and design of experiments. Traditional RSM, as it has been used in practice, employs low-order regression polynomials to model the variation of the aerodynamic quantities, or some measure of optimality, with respect to the design variables. This polynomial model of the objective function in design space is then searched to obtain the optimal design. Several such polynomial models may have to be constructed to traverse the region of design space that lies between the initial design and the optimal design. This method does not suffer from the shortcomings of the methods mentioned above. However, modeling complex functional behaviors using RSM will necessitate the use of high-order polynomials with their attendant problems.
Artificial neural networks have been widely used in aeronautical engineering. Recent aerodynamic applications include, for example, flow control, estimation of aerodynamic coefficients, compact functional representations of aerodynamic data for rapid interpolation, grid generation, and aerodynamic design. Neural networks have been used to both model unsteady flows and to optimize aerodynamic performance parameters. Significant cost savings have been realized in reducing wind tunnel test times by using neural nets to interpolate between measurements. Neural network applications in aeronautics are not limited to aerodynamics and may be applied in structural analysis and design as well as many other technical disciplines.
In order for neural networks to be used effectively in design, it is imperative that the design space be populated both adequately and efficiently with simulation or experimental data. A sparse population results in an inaccurate representation of the objective function in design space while an inefficient use of aerodynamic data in populating the design space could result in excessive simulation costs. Current applications of neural networks are restricted to simple designs involving only a few design parameters because a linear increase in the number of design parameters often results in a geometric increase in the number of datasets required to adequately represent the design space.
Therefore, a need exists for adequately and efficiently populating large-dimensional design spaces to achieve an optimal design. More particularly, to be able to use existing design or experimental data, or partial or unstructured sets of data, to influence the design process. The subject invention herein, solves these problems in a novel manner not previously known in the art.
It is therefore the object of the present invention to provide an improved method and system for design optimization, using composite response surfaces, and having the following characteristics:
ability to start from a generic design that is far from optimal;
easy and economical to use in large dimensional design space;
ability to handle a variety of design objectives;
ability to easily impose constraints, incorporate design guidelines and rules of thumb;
ability to handle both simulation and experimental data simultaneously;
ability to handle partial data sets and data that lack structure;
insensitivity to noise in the data;
ability to handle data of varying fidelity as the design evolves;
ability to handle unsteady data (unsteady effects) in the design process;
flexibility to handle additional data as it becomes available;
ability to rapidly perform design trade-off studies;
ability to leverage the multi-tiered parallelism possible on modern
distributed and parallel computers; and
ability to execute designs that are influenced by multiple disciplines (multi-disciplinary optimization).
The foregoing object is achieved, as is now described, using a method and system that incorporates the advantages of both traditional response surface methodology (RSM) and neural networks. The present invention employs a unique strategy called parameter-based partitioning of the given design space. In the design procedure, a sequence of composite response surfaces based on both neural networks and polynomial fits are used to traverse the design space to identify an optimal solution. The composite response surface has both the power of neural networks and the economy of low-order polynomials (in terms of the number of simulations needed and the network training requirements). The present invention handles design problems with many more parameters than would be possible using neural networks alone and permits a designer to rapidly perform a variety of trade-off studies before arriving at the final design.
The above as well as additional objects, features, and advantages of the present invention will become apparent in the following detailed written description.